Analysis of an $$M/\begin{pmatrix}G_1\\ G_2\end{pmatrix}/1$$ Queue with Bernoulli Vacation and Server Breakdown

This paper addresses a model on a single server queue and two service representatives. After a customer is served, he/she has the three options: opting for receive the same service again (re-service), joining as a new customer for another regular service (feedback), or leaving the service system altogether. To ensure the queueing system is Markovian, we introduce an additional variable (supplementary variable) and using this approach, we derive the explicit distribution of queue size at random and departure epochs. Additionally, we determine the distribution of response time, inter-departure time, and busy period. By using the embedded Markov chain technique we have also derived the queue size distribution at departure epoch. We have also presented the cost analysis of the model with some numerical examples. The numerical illustration validates our findings and provides valuable insights into the queuing system.

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Analysis of an $$M/\begin{pmatrix}G_1\\ G_2\end{pmatrix}/1$$ Queue with Bernoulli Vacation and Server Breakdown

Cited by 5 publications

References 38 publications

A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

Markovian queueing model under Bernoulli vacation and servers’ malfunctioning: Metaheuristic optimization technique

Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

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